Abstract
In this first chapter, I accomplish several goals. First, building on my 20+ years of work on missing data analysis, I outline a nomenclature or system for talking about the theory underlying the modern analysis of missing data. I intend for this nomenclature to be in plain English, but nevertheless to be an accurate representation of statistical theory relating to missing data analysis. Second, I describe many of the main components of missing data theory, including the causes or mechanisms of missingness. Two general methods for handling missing data, in particular multiple imputation (MI) and maximum-likelihood (ML) methods, have developed out of the missing data theory I describe here. And as will be clear from reading this book, I fully endorse these methods. For the remainder of this chapter, I challenge some of the commonly held beliefs relating to missing data theory and missing data analysis, and make a case that the MI and ML procedures, which have started to become mainstream in statistical analysis with missing data, are applicable in a much larger range of contexts that typically believed.
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Notes
- 1.
- 2.
Little and Rubin (2002) refer to this as Not Missing At Random (NMAR). But Schafer and Âcolleagues (Collins et al. 2001; Schafer and Graham 2002) refer to this same mechanism as Missing Not At Random (MNAR). I have decided to use NMAR here, because it makes sense that missingness should either be MAR or not (i.e., Not MAR). However, there are good arguments for using MNAR as well. I view the two terms to be interchangeable.
- 3.
Although as I demonstrate in a later section of this chapter, the amount of bias depends on many factors, and may often be tolerably low.
- 4.
One common variant of Y, for example, could be Z, a 4-level, uniformly distributed variable where the four levels represent the quartiles of the original Y variable, which was continuous and normally distributed. In this example, the two variables are highly correlated (r YZ  =  .925), but they are not correlated r  =  1.0.
- 5.
At the heart of all methods for analysis of NMAR missingness is a guess or assumption about the missing data creation model. Because all such methods must make these assumptions, methods for NMAR missingness are only as good as their assumptions. Please see the discussion in the next section.
- 6.
I describe the range quantity in more detail in Chap. 10. One important point about this quantity is that for any given level of missingness, rZR is a linear transformation of the range of probabilities in the MAR-linear IF statements. During our simulation work (Graham et al. 2008), Lori Palen discovered that rZR was the product of a constant (0.7453559925 for 50 % missingness and Z as uniformly distributed variable with four levels) and the range between the highest and lowest probabilities for the IF statements. I refer to this constant as the Palen proportion.
- 7.
Note that the quartilized version of Smoke10 (Z10), had only three levels in the data used in this example (0, 2, 3). Despite this, however, the results shown in this section are representative of what will commonly be found with these analyses.
- 8.
- 9.
Note that everything I describe in this section can also be applied to the situation in which the predictor variable is a measured variable and not a manipulated program intervention variable.
- 10.
Note that the plots shown in Table 1.1 could also be based on more than two levels of a measured independent variable.
- 11.
Of course, the distinction between main measure and auxiliary variable becomes blurred when the methods used for collecting data on the follow-up sample are the same as, or very similar to, the methods used for the main measure of the DV, and when the follow-up measure occurs at a time not too far removed from the main measure.
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Graham, J.W. (2012). Missing Data Theory. In: Missing Data. Statistics for Social and Behavioral Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4018-5_1
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